Replace the whole set, it's like $5-$10...then you have all new, matched strings.

I'm in agreement, although in five years of playing my ukulele every day I've never broken a string, so I can't speak from experience. But if I did I would change out the whole set. What do you do with the other three strings if you don't? I can guarantee you that if I took one string out of a set, I wouldn't be able to find the other three a week later. But if they are new strings and you break one, I guess that would be a different story. Why am I even answering this question? I've never broken a string to replace it and this is the first time I've ever thought about what I would do if I did. What do I know? Don't listen to me?

you might check for burrs or sharp edges on your tailpiece. A bit of sanding with a tightly rolled up tube of 800 grit wet/dry sandpaper will take care of most.

Nah, the strings were really old. It was the tight first string that popped. I don’t play this banjolele very much any more. It was the the first “banjo type instrument” that I bought. Mostly it just sits around to look at.